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- Feb 14, 2012

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The problem stated below has me stumped. I've been trying to solve it for some times but I kept ended up with zero equals zero kind of silly result and I'd appreciate it if someone could show me some ideas on how to crack it.

Thanks in advance.

Problem:

Let \(\displaystyle a,\;b,\;c\) be roots of equation \(\displaystyle x^3-6x^2+kx+k=0\) and \(\displaystyle (a-1)^3+(b-2)^3+(c-3)^3=0\). Find a, b, c and k.